Law of incipient separation for turbulent flows over airfoils as inferred by RANS

Abstract

In a recent study, Lu, Aithal & Ferrante (AIAA J., 2021) have discovered the law of incipient separation for curved ramps that predicts the incipiency of flow separation by knowing only a few geometrical parameters of the ramp and the Reynolds number of the incoming flow. In the present study, we have searched for a similar law to predict the separation of the turbulent flow over airfoils. With that goal, we have conducted two-dimensional Reynolds averaged Navier-Stokes (RANS) wall-resolved simulations of incompressible turbulent flows over several airfoils over a range of angles of attack. Along the study, we have carried out verification and validation of RANS using the Spalart-Allmaras model against the experimental measurements by Wadcock (NASA-CR-177450, 1987) for the turbulent flow over a NACA4412 airfoil at a Reynolds number based on the airfoil chord length of Re = 1640000. From such comparison, we have found that although the RANS prediction fails when the airfoil approaches its maximum lift (alpha < 12 degrees), the incipient separation occurs at a much smaller angle of attack, i.e., alpha ~ 1 degree. Thus, we have investigated the effects of the angle of attack, airfoil thickness, and camber on the incipiency of flow separation for eleven different airfoils and Re = [1640000, 6000000]. From the RANS results, we have determined a law for predicting the incipiency of turbulent flow separation that relies only on a few key airfoil's geometrical parameters, angle of attack, and the Reynolds number of the flow.